Abstract: We theoretically investigate the apparent contact angle and contact angle
hysteresis of a droplet placed on a liquid infused surface. We show that the
apparent contact angle is not uniquely defined by material parameters, but also
has a strong dependence on the relative size between the droplet and its
surrounding wetting ridge formed by the infusing liquid. We derive a closed
form expression for the contact angle in the limit of vanishing wetting ridge,
and compute the correction for small but finite ridge, which corresponds to an
effective line tension term. We also predict contact angle hysteresis on liquid
infused surfaces generated by the pinning of the contact lines by the surface
corrugations. Our analytical expressions for both the apparent contact angle
and contact angle hysteresis can be interpreted as `weighted sums' between the
contact angles of the infusing liquid relative to the droplet and surrounding
gas phases, where the weighting coefficients are given by ratios of the fluid
surface tensions.